Hey guys, I'm in a college trig class and these questions were on my last test. I thought I had trig identities down but I barely know where to start on these ones. Can you help me out?
1. 12sin(2t)cos(3t)+20sin(2t)-cos(3t)-5=0
2. 6sec(2t)^2-13sec(2t)=6
3. 2sin(x)cos(-x)=2sin(-x)sin(x)
For no. 3 Use cos(-x)=cosx and sin(-x)=-sinx
So question becomes 2sinxcosx=-2sinxsinx Cancel 2 and get sinxcosx+sinxsinx=0
sinx(cosx+sinx)=0 So sinx=0 or cosx+sinx=0 giving sinx=-cosx giving sinx/cosx=-1 That is tanx=-1
So sinx-0 or tanx=-1 Give the answers for x in whatever range you were asked.